Leisha Hailey has racked up a lot of media attention after she was kicked off of a Southwest flight on Sunday for being gay. The L- Word star immediately took to twitter to urge others to boycott the airline.

The 40-year-old star, who started her career as a musician, is best known for her role as bisexual writer Alice on the hit Showtime series L- Word, which follows the lives of a group of lesbian and bisexual friends.

She took to twitter on Monday with a firestorm of tweets about Southwest:

I have been discriminated against by @SouthwestAir. Flt. attendant said that it was a family airline and kissing was not ok.

This is an outrage. I demand a public apology by @SouthwestAir and a refund. Hate is not a family value. I will never fly this airline.

We were escorted off the plane for getting upset about the issue. @SouthwestAir endorses homophobic employees. No one made her accountable.

Since when is showing affection towards someone you love illegal? I want to know what Southwest Airlines considers as family.

I know plenty of wonderful same sex families I would like to introduce them to. Boycott @SouthwestAir if you are gay. They don't like us.

Did I mention to @SouthwestAir that I have a lot of their actions recorded on audio and video? RT #boycottSouthwest #discrimination

This is a hoot @leisha_hailey @uhhuhhermusic Southwest Airlines The LUV Airline! the 'luv' airline. what kind of 'luv' are ya talkin bout? Sandra Bernhard tweeted.

Yet, why the star and her girlfriend Camila Grey were kicked off the plane remains in dispute.

Hailey claims that she was removed from the aircraft in El Paso, Texas after a flight attendant stopped her from kissing her girlfriend, saying that it was a 'family' airline and kissing was not OK.

Southwest claims that the issue was best solved outside the plane and that passengers had complained about the kissing, characterizing it as excessive.

The conversation escalated to a level that was better resolved on the ground, as opposed to in flight, the airline explained in a statement Tuesday morning.

We regret any circumstance where a passenger does not have a positive experience on Southwest and we are ready to work directly with the passengers involved to offer our heartfelt apologies for falling short of their expectation, Southwest added.

With increased media attention on Tuesday, both parties issued further statements.

In no way were our actions on Southwest Airlines excessive, inappropriate or vulgar. We want to make it clear we were not making out or creating any kind of spectacle of ourselves, it was one, modest kiss. We are responsible adult women who walk through the world with dignity. We were simply being affectionate like any normal couple. We were on the airplane less than 5 minutes when all was said and done, Hailey and Grey said in a joint statement released Tuesday afternoon.

We find it very disturbing that the same airline who lauds itself as being LGBT friendly has twisted an upsetting incident that happened into our behavior being 'too excessive,' they said, adding No matter how quietly homophobia is whispered, it doesn't make it any less loud. You can't whisper hate. We ask this airline to teach their employees to not discriminate against any couple, ever, regardless of their own beliefs.

The pair said that they were filing a formal complaint with the airline.

Southwest, a company that prides itself on being LGBT friendly, fought back Tuesday evening with its own statement.

Additional reports from our Employees and Customers onboard flight 2274 during a stop in El Paso on Sunday now confirm profane language was being used loudly by two passengers. At least one family who was offended by the loud profanity moved to another area of the cabin, the statement said. Although we have reports of what Customers characterize as an excessive public display of affection, ultimately their aggressive reaction led to their removal from the aircraft. We do not tolerate discrimination against anyone for any reason. In this situation, their removal was directly and solely related to the escalated conversation that developed onboard the aircraft.

Our tenets of inclusion and celebration of diversity among our Customers and Employees-including those in the LGBT communities-anchor our Culture of mutual respect and following the Golden Rule, the statement continued. The more than 100 million people who fly Southwest each year reflect the great diversity of our country and our Company - and ALL are valued and welcome. In fact, we've been recognized as a leader in diversity throughout our 40 years of service.